We have investigated the weak absorption lines of CO2 (2003 ← 0000) R(6), C2H2 (2100011 ← 0000000) R(12), and C2H2 (1200031 ← 0000000) P(6) near 1064 nm using CW cavity ring-down spectroscopy and CW cavity transmission. An effective interaction length of more than 30 km was achieved (cavity finesse ≈ 86 000) and the sensitivity was ≈ 10-8 cm-1. Higher sensitivity of 3.3 × 10-11 cm-1/√Hz was obtained by cavity-enhanced wavelength modulation spectroscopy. The absorption coefficients, pressure broadening coefficients, lineshapes, line strengths, and absolute wavelengths of those lines were determined, some of them for the first time. The measurements were carried out over a wide range of pressures from the strongly inhomogeneous to the strongly homogeneous region.